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I'm surprised that nobody has mentioned Serre's Corps locaux (Local FieldsFields), his Cohomologie galoisienne (Galois cohomology) and his Représentations linéaires des groupes finis (Linear representations of finite groups).

Other eternal texts in Number Theory include Artin's Algebraic numbers and algebraic functions and the Artin-Tate notes on Class field theory, Hasse's Zahlentheorie and his Klassenkörperbericht, Hecke's Vorlesungen über die Theorie der Algebraischen Zahlen, Weyl's Algebraic Theory of Numbers, and Hilbert's Zahlbericht.

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I'm surprised that nobody has mentioned Serre's Corps locaux (Local Fields) and his Représentations linéaires des groupes finis (Linear representations of finite groups). Other eternal texts in Number Theory include Artin's Algebraic numbers and algebraic functions and the Artin-Tate notes on Class field theory, Hasse's Zahlentheorie and his Klassenkörperbericht, Hecke's Vorlesungen über die Theorie der Algebraischen Zahlen, Weyl's Algebraic Theory of Numbers, and Hilbert's Zahlbericht.